Polynomial Entropies and Integrable Hamiltonian Systems

    2013, Volume 18, Number 6, pp.  623-655

    Author(s): Marco J.

    We introduce two numerical conjugacy invariants of dynamical systems — the polynomial entropy and the weak polynomial entropy — which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants describe the polynomial growth rate of the number of balls (for the usual "dynamical" distances) of covers of the ambient space. We give explicit examples of computation of these polynomial entropies for generic Hamiltonian systems on surfaces.
    Keywords: dynamical complexity, entropy, integrability, Morse Hamiltonians
    Citation: Marco J., Polynomial Entropies and Integrable Hamiltonian Systems, Regular and Chaotic Dynamics, 2013, Volume 18, Number 6, pp. 623-655

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